Accurate Multi-Phase Flow Simulation in Faulted Reservoirs Using Mimetic Finite Difference Methods on Polyhedral Cells

Faulted reservoirs are commonly modeled by corner-point grids. Since the two-point flux approximation (TPFA) method is not consistent on non-orthogonal grids, multi-phase flow simulation using TPFA on corner-point grids may have significant discretization errors if grids are not K-orthogonal. To improve the simulation accuracy, we developed a novel method where the faults are modeled by polyhedral cells, and mimetic finite difference (MFD) methods are used to solve flow equations. We use a cut-cell approach to build the mesh for faulted reservoirs. A regular orthogonal grid is first constructed,and then fault planes are added by dividing cells at fault planes. Most cells remain orthogonal while irregular non-orthogonal polyhedral cells can be formed with multiple cell divisions. We investigated three spatial discretization methods for solving the pressure equation on general polyhedral grids, including the TPFA, MFD and TPFA-MFD hybrid methods. In the TPFA-MFD hybrid method, the MFD method is only applied to part of the domain while the TPFA method is applied to rest of the domain. We compared flux accuracy between TPFA and MFD methods by solving a single-phase flow problem. The reference solution is obtained on a rectangular grid while the same problem is solved by TPFA and MFD methods on a grid with distorted cells near a fault. Fluxes computed using TPFA exhibit larger errors in the vicinity of the fault while fluxes computed using MFD are still as accurate as the reference solution. We also compared saturation accuracy of two-phase (oil and water) flow in faulted reservoirs when the pressure equation is solved by different discretization methods. Compared with the reference saturation solution, saturation exhibits non-physical errors near the fault when pressure equation is solved by the TPFA method. Since the MFD method yields accurate fluxes over general polyhedral grids, the resulting saturation solutions match the reference saturation solutions with an enhanced accuracy when the pressure equation is solved by the MFD method. Based on the results of our simulation studies, the accuracy of the TPFA-MFD hybrid method is very close to the accuracy of the MFD method while the TPFA-MFD hybrid method is computationally cheaper than the MFD method.